next up previous contents
Next: Projection pursuit. Up: Linear projection methods Previous: Linear projection methods

Principal component analysis

(PCA) [Hotelling, 1933] can be used to display the data as a linear projection on such a subspace of the original data space that best preserves the variance in the data. It is a standard method in data analysis; it is well understood, and effective algorithms exist for computing the projection. Even neural algorithms exist [Oja, 1983, Oja, 1992, Rubner and Tavan, 1989, Cichocki and Unbehauen, 1993]. A demonstration of PCA is presented in Figure 2.

Figure: A dataset projected linearly onto the two-dimensional subspace obtained with PCA. Each 39-dimensional data item describes different aspects of the welfare and poverty of one country. The data set consisting of 77 countries, used also in Publication 2, was picked up from the World Development Report published by the World Bank (1992). Missing data values were neglected when computing the principal components, and zeroed when forming the projections. A key to the abbreviated country names is given in the Appendix.

Sami Kaski
Mon Mar 31 23:43:35 EET DST 1997